Traditionally, Bayesian network structure learning is often carried out at a central site, in which all data is gathered. However, in practice, data may be distributed across different parties (e.g., companies, devices) who intend to collectively learn a Bayesian network, but are not willing to disclose information related to their data owing to privacy or security concerns. In this work, we present a cross-silo federated learning approach to estimate the structure of Bayesian network from data that is horizontally partitioned across different parties. We develop a distributed structure learning method based on continuous optimization, using the alternating direction method of multipliers (ADMM), such that only the model parameters have to be exchanged during the optimization process. We demonstrate the flexibility of our approach by adopting it for both linear and nonlinear cases. Experimental results on synthetic and real datasets show that it achieves an improved performance over the other methods, especially when there is a relatively large number of clients and each has a limited sample size.

本文提出一种基于联邦学习的方法，用于估计来自不同方的数据 横向分割后的 贝叶斯网络结构。该方法采用基于连续优化的分布式结构学习方法，使用多重乘法器的交替方向方法（ADMM），在优化过程中仅交换模型参数，实现了数据隐私的保护。实验结果表明，该方法在合成和实际数据集上的性能优于其他方法，特别是在客户端数量相对较多且每个客户端的样本量有限的情况下。

基于连续优化的联邦贝叶斯网络结构学习